ASPEN AEROGELS,INC. COMMON STOCK PURCHASE WARRANT

Exhibit 4.2

THIS WARRANT AND ANY SECURITIES ACQUIRED UPON THE EXERCISE OF THIS WARRANT HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “ACT”), OR ANY APPLICABLE STATE SECURITIES LAWS. NEITHER THIS WARRANT, SUCH SECURITIES NOR ANY INTEREST THEREIN MAY BE TRANSFERRED EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER THE ACT AND APPLICABLE STATE SECURITIES LAWS OR PURSUANT TO AN APPLICABLE EXEMPTION FROM THE REGISTRATION REQUIREMENTS OF THE ACT AND APPLICABLE STATE SECURITIES LAWS.

THE SALE, ASSIGNMENT, HYPOTHECATION, PLEDGE, ENCUMBRANCE OR OTHER DISPOSITION AND VOTING OF ANY OF THE SHARES OF COMMON STOCK OF THE COMPANY ACQUIRED PURSUANT TO THE EXERCISE OF THIS WARRANT ARE RESTRICTED BY THE TERMS OF THE THIRD AMENDED AND RESTATED STOCKHOLDERS’ AGREEMENT, DATED AS OF JUNE 10, 2008, AMONG THE COMPANY AND CERTAIN OF ITS STOCKHOLDERS. THE COMPANY WILL NOT REGISTER THE TRANSFER OF SUCH SHARES OF COMMON STOCK ON THE BOOKS OF THE COMPANY UNLESS AND UNTIL THE TRANSFER HAS BEEN MADE IN COMPLIANCE WITH THE TERMS OF THE STOCKHOLDERS AGREEMENT, A COPY OF WHICH WILL BE PROVIDED AT NO COST TO THE HOLDER HEREOF UPON WRITTEN REQUEST TO THE COMPANY.

ASPEN AEROGELS, INC.

COMMON STOCK PURCHASE WARRANT

This document (this “Warrant”) certifies that, for good and valuable consideration, Aspen Aerogels, Inc., a Delaware corporation (the “Company”), grants to [IMPORT WARRANTHOLDER] (the “Warrantholder”), the right to subscribe for and purchase from the Company, on or before [IMPORT EXPIRATION TIME] (the “Expiration Time”), an aggregate of [IMPORT SHARE NUMBERS] validly issued, fully paid and nonassessable shares of Common Stock (the “Warrant Shares”), at the exercise price per share of $4.423 (the “Exercise Price”), all subject to the terms, provisions, conditions and adjustments (including adjustments to number of shares and Exercise Price) herein set forth. The Company acknowledges that the cash consideration paid by Warrantholder for this Warrant is $10.00 for income tax purposes, that such amount has been duly received by the Company, and that this Warrant is issued in connection with that certain financial accommodation entered into by and between Company as the obligor and Warrantholder as the obligee thereunder (the “Financing Arrangement”) and that this Warrant amends and restates all warrants previously issued to the Warrantholder in connection with the Financing Arrangement. Capitalized terms used herein which are not specifically defined in other sections of this Warrant, shall have the meanings set forth in Section 11.

1. Warrant Term. The purchase rights represented by this Warrant are exercisable, in whole or in part, at any time and from time to time, from and after the Warrant grant date of [IMPORT GRANT DATE], and on or prior to the earlier of the (i) Expiration Time, or (ii) in the event of a Corporate Event.

2. Exercise of Warrant; Payment of Taxes.

2.1 Exercise of Warrant. The purchase rights represented by this Warrant may be exercised by the Warrantholder, in whole or in part and from time to time, by the surrender of this Warrant (with a duly executed notice of exercise form, the “Exercise Form”, in the form attached hereto as Exhibit A) at the principal office of the Company and by the payment to the Company of an amount equal to the then applicable Exercise Price per share multiplied by the number of Shares then being purchased. If the Warrantholder is not already a party thereto, the Warrantholder shall also execute, upon request from the Company, a joinder agreement to the Stockholder’s Agreement, as amended and restated, such joinder agreement to be in form and substance mutually agreeable to both Warrantholder and Company. The Warrantholder shall be deemed to have become the holder(s) of record of, and shall be treated for all purposes as the record holder(s) of, the Shares represented thereby (and such Shares shall be deemed to have been issued) immediately prior to the close of business on the date or dates upon which this Warrant is exercised.

2.2 Non-Cash Exercise.

(a) In lieu of payment in cash, the rights represented by this Warrant may also be exercised at any time by a written notice of exercise in the form of Exhibit A attached hereto, providing for the non-cash exercise of this Warrant for the Shares equal to the value (as determined below) of this Warrant (or the portion thereof being exercised), specifying that this non-cash exercise election has been made, and the net number of Shares to be issued after giving effect to such non-cash exercise. In the event the Warrantholder makes such election, Company shall issue to the holder a number of shares computed using the following formula:

Where:

X = the number of Shares to be issued to the holder

Y = the number of Shares purchasable under the Warrant or, if only a portion of the Warrant is being exercised, the portion of the Warrant being exercised (as of the date of such non-cash exercise)

A = the Fair Market Value of one Share of Common Stock (as of the date of such non-cash exercise)

B = Exercise Price of one Share of Common Stock (as adjusted to the date of such non-cash exercise)

(b) For purposes of this Section 2.2, the “Fair Market Value” of one share of the Company’s Common Stock shall be equal to either (i) if the exercise of this Warrant occurs in connection with an initial public offering of the Company, then the Fair Market Value shall be equal to the “initial price to public” specified in the final prospectus with respect to the initial public offering, or (ii) if the exercise of this Warrant occurs after an initial public offering of the Company but not in connection therewith, then the Fair Market Value shall be equal to the average of the closing price(s) of the Company’s Common Stock as quoted over the counter or on any exchange on which the Common Stock is listed as such closing prices are published in The Wall Street Journal for the fifteen trading days (or such

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lesser number of trading days as the stock may have been actually trading) ending on the day prior to the date of determination of Fair Market Value. Notwithstanding the foregoing, if the Warrant is exercised in connection with a merger or sale of all or substantially all of the Company’s assets, Fair Market Value shall mean the value that would have been allocable to or received in respect of a Warrant Share had the Warrant been exercised prior to such merger or sale. If the Common Stock is not traded Over The Counter or on an exchange, or if the Warrant is not exercised in connection with a merger or sale of all or substantially all of its assets, then the Fair Market Value shall be determined in good faith by the Company’s board of directors. If the holder hereof does not agree with the determination of Fair Market Value as determined by the Company’s board of directors, the Company and the holder hereof shall negotiate an appropriate Fair Market Value. If after ten (10) days, the Company and the holder cannot agree, then the holder may request that the Fair Market Value be determined by an investment banker of national reputation selected by the Company and reasonably acceptable to the Warrantholder. The fees and expenses of such investment banker shall be borne by the Company unless the Fair Market Value determined by such investment banker is equal to or less that the Fair Market Value as determined by the Company, in which event the fees and expenses of such investment banker shall be borne by the holder hereof.

2.3 Automatic Exercise. Immediately before the expiration or termination of this Warrant, to the extent this Warrant is not previously exercised, and if the Fair Market Value of one share of the Company’s Common Stock subject to this Warrant is greater than the Exercise Price, then in effect as adjusted pursuant to this Warrant, this Warrant shall be deemed automatically exercised pursuant to Section 2.2 above, even if not surrendered. For purposes of such automatic exercise, the Fair Market Value of the Company’s Common Stock upon such expiration shall be determined pursuant to Section 2.2 (b) above. To the extent this Warrant or any portion thereof is deemed automatically exercised pursuant to this Section, the Company agrees to promptly notify the Warrantholder of the number of Shares, if any, the holder hereof is to receive by reason of such automatic exercise.

2.4 Exercise in Connection with an Initial Public Offering, Sale or Merger. Notwithstanding any other provision hereof, if the exercise of all or any portion of this Warrant is made or to be made in connection with the occurrence of a public offering, sale or merger of the Company, the exercise of all or any portion of this Warrant shall, at the election of the Warrantholder, be conditioned upon the consummation of the public offering, sale or merger of the Company in which case such exercise shall not be deemed to be effective until the consummation of such transaction. In the event that transaction is not consummated within 45 days of the targeted date of the transaction, any such exercise shall, at the election of the Warrantholder, be deemed rescinded.

2.5 Warrant Shares Certificate. A stock certificate for the Warrant Shares specified in the Exercise Form shall be delivered to the Warrantholder within five (5) Business Days after receipt of the Exercise Form by the Company and payment by the Warrantholder of the aggregate Exercise Price (or non-cash exercise in lieu of payment as permitted in Section 2.2), along with a check from the Company in lieu of any fractional shares which the Warrantholder would be entitled to purchase under this Warrant. If this Warrant was exercised in part, the Company shall, at the time of delivery of the stock certificate, deliver to the Warrantholder a new Warrant evidencing the right to purchase the remaining Warrant Shares, which new Warrant shall in all other respects be identical with this Warrant.

2.6 Payment of Taxes. The Company shall pay all expenses, taxes and other governmental charges with respect to the issue or delivery of the Warrant Shares, unless such tax or charge is imposed by law upon the Warrantholder.

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3. Restrictions on Transfer; Restrictive Legends.

3.1 Restrictions on Transfer. This Warrant and the Warrant Shares issuable upon exercise of all or part of this Warrant are unregistered securities that are subject to the restrictions on transfer imposed by the Securities Act and applicable state securities laws and may not be offered, sold, transferred, pledged or otherwise disposed of, in whole or in part, to any Person other than in accordance with the Securities Act and applicable state securities laws. The Warrant Shares issuable upon exercise of all or part of this Warrant are also subject to additional restrictions on transfer set forth in the Stockholders Agreement and may not be offered, sold, transferred, pledged or otherwise disposed of, in whole or in part, to any Person other than in accordance with the Stockholders Agreement.

3.2 Restrictive Legends. Until such time as the restrictions on transfer imposed on this Warrant by the Securities Act and applicable state securities laws shall no longer be effective, this Warrant, any Warrant issued to the Warrantholder upon the partial exercise of this Warrant pursuant to Section 2, and any Warrant issued to the Warrantholder in substitution for this Warrant pursuant to Section 7 shall be stamped or otherwise imprinted with a legend in substantially the form as set forth on the cover of this Warrant. Until such time as the restrictions on transfer imposed on the Warrant Shares by the Securities Act, applicable state securities laws and the Stockholders Agreement shall no longer be effective, each stock certificate for Warrant Shares and each stock certificate issued upon the direct or indirect transfer of any such Warrant Shares shall be stamped or otherwise imprinted with a legend in substantially the form provided in the Stockholders’ Agreement. Upon the termination of such restrictions on transfer, the Warrantholder may require the Company to issue a Warrant or a stock certificate for Warrant Shares, in each case without a legend, if and to the extent permitted by, and in accordance with, the Stockholders Agreement and applicable law.

4. Reservation and Registration of Shares. The Company covenants and agrees as follows:

4.1 Validly Issued and Free of Encumbrances. All Warrant Shares issued upon the exercise of all or any part of this Warrant shall, upon issuance and payment of the Exercise Price therefore (or upon non-cash exercise as permitted herein), be validly issued, fully paid and nonassessable, issued in compliance with all applicable federal and state securities laws, and free from all taxes, liens and charges with respect to the issue thereof, and not subject to any preemptive rights.

4.2 Sufficient Authorized Shares. During the period within which the rights represented by this Warrant may be exercised, the Company shall at all times have authorized and reserved, for the purpose of issuance of Common Stock upon any exercise of the purchase rights evidenced by this Warrant, and shall keep available free from preemptive rights, a sufficient number of shares of its Common Stock to provide for the exercise of the rights represented by this Warrant.

4.3 Noncontravention. The Company shall not, by amendment of its Certificate of Incorporation or through any reorganization, transfer of assets, spin-off, consolidation, merger, dissolution, issue or sale of securities or any other action or inaction, avoid or seek to avoid the observance or performance of any of the terms of this Warrant to be observed or performed hereunder, and shall at all times in good faith assist in performing, carrying out, and giving effect to the terms hereof and in the taking of all such actions as may be necessary or appropriate in order to protect the rights of the Warrantholder against dilution or other impairment.

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5. Anti-Dilution Adjustments. From and after the date hereof and until the Expiration Date, notwithstanding the fact that no Warrant Shares shall be issued and outstanding, the Exercise Price, and the number and type of Warrant Shares or other securities to be received upon exercise of the Warrant, shall be subject to adjustment as follows:

5.1 Dividend, Subdivision, Combination or Reclassification of Common Stock. If the Company shall, at any time or from time to time, prior to exercise in full of this Warrant: (a) pay a dividend or otherwise make a distribution on the outstanding shares of Common Stock payable in Capital Stock; (b) subdivide the outstanding shares of Common Stock into a larger number of shares; (c) combine the outstanding shares of Common Stock into a smaller number of shares; or (d) issue any shares of its Capital Stock in a reclassification of the Common Stock (other than any such event for which an adjustment is made pursuant to another clause of this Section 5), then, and in each such case, the Exercise Price and the number of Warrant Shares exercisable hereunder in effect immediately prior to such event shall be adjusted (and any other appropriate actions shall be taken by the Company) so that the Warrantholder shall thereafter be entitled to receive, upon the exercise of the unexercised portion of this Warrant, the number of shares of Common Stock or other securities of the Company that such Warrantholder would have owned or would have been entitled to receive upon or by reason of any of the events described above, had this Warrant been exercised immediately prior to the occurrence of such event. An adjustment made pursuant to this Section 5.1 shall become effective retroactively: (x) in the case of any such dividend or distribution, to a date immediately following the close of business on the record date for the determination of holders of Common Stock entitled to receive such dividend or distribution; or (y) in the case of any such subdivision, combination or reclassification, to the close of business on the day upon which such corporate action becomes effective.

5.2 Issuance of Common Stock or Common Stock Equivalents below Exercise Price. If the Company shall, at any time or from time to time, prior to exercise in full of this Warrant, issue or sell any shares of Common Stock or Common Stock Equivalents at a “New Issue Price” (as defined below) per share of Common Stock or Common Stock Equivalent that is less than the Exercise Price then in effect as of the record date or Issue Date referred to in the following sentence, as the case may be (the “Relevant Date”), other than issuances of Excluded Stock, then, and in each such case, the Exercise Price then in effect shall be adjusted by multiplying the Exercise Price in effect immediately prior to the Relevant Date by a fraction:

(a) the numerator of which shall be the sum of the number of shares of Common Stock outstanding on the Relevant Date (assuming conversion or exercise of all Common Stock Equivalents into Common Stock) plus (i) in the case of Common Stock, the number of shares of Common Stock which the aggregate consideration received by the Company for the total number of such additional shares of Common Stock so issued would purchase at the Exercise Price on the Relevant Date, or (ii) in the case of Common Stock Equivalents, the number of shares of Common Stock which the aggregate amount of the consideration paid for, or the aggregate exercise price of, such Common Stock Equivalents, plus any additional consideration payable upon conversion, exchange or exercise of such Common Stock Equivalents, would purchase at the Exercise Price on the Relevant Date; and

(b) the denominator of which shall be the sum of (i) the number of shares of Common Stock outstanding on the Relevant Date (assuming conversion or exercise of all Common Stock Equivalents into Common Stock) plus (ii) the number of additional shares of Common Stock issued or to be issued or, in the case of Common Stock Equivalents, the maximum number of shares of Common Stock into which such Common Stock Equivalents initially may convert, exchange or be exercised.

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Such adjustment shall be made whenever such shares of Common Stock or Common Stock Equivalents are issued, and shall become effective retroactively, in the case of an issuance to the stockholders of the Company, as such, to a date immediately following the close of business on the record date for the determination of stockholders entitled to receive such shares of Common Stock or Common Stock Equivalents, and, in all other cases, on the date of such issuance (the “Issue Date”); provided, however, that the determination as to whether an adjustment is required to be made pursuant to this Section 5.2 shall only be made upon the issuance of such shares of Common Stock or Common Stock Equivalents, and not upon the issuance of any security into which the Common Stock Equivalents convert, exchange or may be exercised. For purposes of this Section 5.2, the “New Issue Price” of any shares of Common Stock shall be equal to the price per share received by the Company upon the consummation of such sale and the “New Issue Price” of any Common Stock Equivalents shall be equal to (x) the sum of (A) the price for such Common Stock Equivalent plus (B) any additional consideration payable (without regard to any anti-dilution adjustments) upon the conversion, exchange or exercise of such Common Stock Equivalent, divided by (y) the number of shares of Common Stock initially underlying such Common Stock Equivalent.

5.3 Certain Distributions. If the Company shall, at any time or from time to time, prior to exercise in full of this Warrant, distribute to all holders of shares of the Common Stock (including any such distribution made in connection with a merger or consolidation in which the Company is the resulting or surviving Person and the Common Stock is not changed or exchanged) cash, evidences of indebtedness of the Company or another issuer, securities of the Company or another issuer or other assets or rights or warrants to subscribe for or purchase securities of the Company (excluding those distributions in respect of which an adjustment in the Exercise Price is made pursuant to another paragraph of this Section 5), then, and in each such case:

(a) the Exercise Price then in effect shall be adjusted (and any other appropriate actions shall be taken by the Company) by multiplying the Exercise Price in effect immediately prior to the date of such distribution by a fraction, (i) the numerator of which shall be the Current Market Price of the Common Stock immediately prior to the date of distribution less the then fair market value (as determined by the Board of Directors in the exercise of their fiduciary duties) of the portion of the cash, evidences of indebtedness, securities or other assets so distributed or of such rights or warrants applicable to one share of Common stock, and (ii) the denominator of which shall be the Current Market Price of the Common Stock immediately prior to the date of distribution (but such fraction shall not be greater than one); provided, however, that no adjustment shall be made upon such distribution pursuant to this Section 5.3(a) if an adjustment is made upon such distribution pursuant to Section 6; and

(b) the number of Warrant Shares for which this Warrant is exercisable immediately prior to such distribution shall be adjusted (and any other appropriate actions shall be taken by the Company) by multiplying the then-current number of Warrant Shares in effect immediately prior to the date of such distribution by a fraction, (i) the numerator of which shall be the Exercise Price in effect immediately prior to immediately prior to the date of distribution, and (ii) the denominator of which shall be the adjusted Exercise Price as determined pursuant to clause (a) of this Section 5.3 (but such fraction shall not be less than one); provided, however, that no adjustment shall be made upon such distribution pursuant to this Section 5.3(b) if an adjustment is made upon such distribution pursuant to Section 6.

Such adjustments shall be made whenever any such distribution is made and shall become effective retroactively to a date immediately following the close of business on the record date for the determination of stockholders entitled to receive such distribution.

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5.4 Other Changes. INTENTIONALLY DELETED

5.5 De Minimus Adjustments. Notwithstanding anything herein to the contrary, no adjustment under this Section 5 need be made to the Exercise Price and the number of Warrant Shares unless such adjustment would require an increase or decrease of at least one percent (1%) of the Exercise Price then in effect. Any lesser adjustment shall be carried forward and shall be made at the time of and together with the next subsequent adjustment which, together with any adjustment or adjustments so carried forward, shall amount to an increase or decrease of at least one percent (1%) of such Exercise Price. Any adjustment to the Exercise Price and the number of Warrant Shares carried forward and not theretofore made shall be made immediately prior to the exercise of this Warrant.

5.6 Notice of Adjustment under Section 5. The Company shall, no later than twenty (20) Business Days prior to the occurrence of any event that would result in an adjustment pursuant to this Section 5, provide the Warrantholder with a written notice describing such event in reasonable detail and setting forth the Exercise Price and number of Warrant Shares, as adjusted as a result of such event.

5.7 Reclassification, Reorganization, Change or Conversion. In case of any reclassification, reorganization, change or conversion of securities of the class issuable upon exercise of this Warrant (other than a change in par value, or from par value to no par value, or from no par value to par value, or as a result of a subdivision or combination), then in any of these events, the Company shall execute a replacement warrant (a “New Warrant”), in form and substance reasonably satisfactory to the holder of this Warrant, upon the exercise of which (and at a total purchase price under the New Warrant not to exceed that payable upon the exercise in full of this Warrant) the holder of the New Warrant shall receive, in lieu of each Share receivable upon the exercise of this Warrant, the same kind and amount of shares of stock, other securities, money and property receivable by a holder of one share of Common Stock upon such reclassification, reorganization, change or conversion. Such New Warrant shall provide for adjustments that shall be as nearly equivalent as may be practicable to the adjustments provided for in this Section 5. The provisions of this section 5.7 shall similarly apply to successive reclassifications, reorganizations, changes, or conversions.

Whenever the Exercise Price shall be adjusted pursuant to the provisions of this Warrant, the Company shall within ten (10) days of such adjustment deliver a certificate signed on behalf of the Company by its chief financial officer to the Warrantholder setting forth, in reasonable detail, the event requiring the adjustment, the amount of the adjustment, the method by which such adjustment was calculated, and the Exercise Price after giving effect to such adjustment.

6. Intentionally Deleted.

7. Exercise or Termination upon Corporate Event. The Company shall, no later than twenty (20) Business Days prior to the anticipated consummation date of any Corporate Event, provide the Warrantholder with a written notice describing such Corporate Event in reasonable detail and setting forth the consideration (i.e., securities, cash and other property) receivable for each share of Common Stock pursuant to such Corporate Event. If the aggregate Exercise Price, as of such consummation date, is equal to or greater than the aggregate value of the securities, cash and other property that would have been received in connection with Corporate Event by a holder of the number of shares of Common Stock for which this Warrant was exercisable immediately prior to such Corporate Event (the “Exercise Proceeds”), then this Warrant shall terminate upon the consummation of such Corporate Event. If the aggregate Exercise Price, as of such consummation date, is less than the aggregate value of the Exercise Proceeds, then the Warrantholder shall be entitled to exercise this Warrant in connection with such Corporate Event and shall automatically receive upon the consummation of such Corporate Event, in lieu of the Warrant Shares, the Exercise Proceeds.

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8. Loss or Destruction of Warrant. Subject to the terms and conditions hereof, upon receipt by the Company of evidence reasonably satisfactory to it of the loss, theft, destruction or mutilation of this Warrant and, in the case of loss, theft or destruction, of such bond or indemnification as the Company may reasonably require, and, in the case of such mutilation, upon surrender and cancellation of this Warrant, the Company will execute and deliver to the Warrantholder a new Warrant of like tenor.

9. Ownership of Warrant. The Company may deem and treat the person in whose name this Warrant is registered as the holder and owner hereof (notwithstanding any notations of ownership or writing hereon made by anyone other than the Company) for all purposes and shall not be affected by any notice to the contrary, until presentation of this Warrant for registration of transfer.

10. Amendments. Any provision of this Warrant may be amended and the observance thereof waived only with the written consent of the Company and the Warrantholder.

11. Definitions. As used herein, unless the context otherwise requires, the following terms have the following respective meanings:

“Affiliate” means, (1) with respect to any Person, any of (a) a director, officer or stockholder holding 5% or more of the capital stock (on a fully diluted basis) of such Person, (b) a spouse, parent, sibling or descendant of such Person (or a spouse, parent, sibling or descendant of any director or officer of such Person) and (c) any other Person that, directly or indirectly through one or more intermediaries, controls, or is controlled by, or is under common control with, another Person or (2) in any event, any Person meeting the definition of “Affiliate” set forth in Rule 405 under the Securities Act. The term “control” includes, without limitation, the possession, directly or indirectly, of the power to direct the management and policies of a Person, whether through the ownership of voting securities, by contract or otherwise.

“Board of Directors” means the Board of Directors of the Company.

“Business Day” means any day other than a Saturday, Sunday or a day on which national banks are authorized by law to close in the Commonwealth of Massachusetts.

“Capital Stock” means, with respect to any Person, any and all shares, interests, participation, rights in, or other equivalents (however designated and whether voting or non-voting) of, such Person’s capital stock and any and all rights, warrants or options exchangeable for or convertible into such capital stock (but excluding any debt security whether or not it is exchangeable for or convertible into such capital stock).

“Common Stock” means the Company’s presently authorized Common Stock, and any stock into or for which such Common Stock may hereafter be converted or exchanged pursuant to the Certificate of Incorporation of the Company as amended from time to time as provided by law and in such Certificate of Incorporation.

“Common Stock Equivalent” means any security or obligation which is by its terms convertible into shares of Common Stock or another Common Stock Equivalent, including, without limitation, any option, warrant or other subscription or purchase right with respect to Common Stock.

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“Corporate Event” means: (i) the sale, transfer, exchange or other disposition in one transaction or a series of related transactions of all or substantially all of the Company’s assets; (ii) any merger, consolidation or other corporate reorganization in one transaction or a series of related transactions that results in the stockholders of the Company immediately prior to such transaction holding less than fifty percent (50%) of the voting power of the surviving entity of such transaction; (iii) the dissolution or liquidation of the Company; or (iv) the sale, transfer, exchange or other disposition in one transaction or a series of related transactions of all or substantially all of the Company’s Common Stock, but does not include any one transaction or series of related transactions the sole purpose and effect of which is to change the state or type of organization of the Company (e.g., to change the Company from a Delaware corporation to a New York corporation or from a corporation to a limited liability company).

“Current Market Price” per share shall mean, as of the date of determination, (a) the average of the daily Market Price under clause (a), (b) or (c) of the definition thereof of the Common Stock during the immediately preceding thirty (30) trading days ending on such date, and (b) if the Common Stock is not then listed or admitted to trading on any national securities exchange or quoted in the over-the-counter market, then the Market Price under clause (d) of the definition thereof on such date.

“Exchange Act” means the Securities Exchange Act of 1934, as amended.

“Excluded Stock” has the meaning set forth in the Stockholders Agreement.

“Market Price” shall mean, as of the date of determination, (a) the closing price per share of Common Stock on such date published in The Wall Street Journal or, if no such closing price on such date is published in The Wall Street Journal, the average of the closing bid and asked prices on such date, as officially reported on the principal national securities exchange (including, without limitation, The Nasdaq Stock Market, Inc.) on which the Common Stock is then listed or admitted to trading; or (b) if the Common Stock is not then listed or admitted to trading on any national securities exchange but is designated as a national market system security by the National Association of Securities Dealers, Inc., the last trading price of the Common Stock on such date; or (c) if there shall have been no trading on such date or if the Common Stock is not so designated, the average of the reported closing bid and asked prices of the Common Stock on such date as shown by the National Market System of the National Association of Securities Dealers, Inc. Automated Quotations System and reported by any member firm of the New York Stock Exchange selected by the Company; or (d) if none of clauses (a), (b) or (c) is applicable, a market price per share determined at the Company’s expense by an appraiser chosen by the Warrantholder, or, if no such appraiser is so chosen more than ten (10) Business Days after notice of the necessity of such calculation shall have been delivered by the Company to the Warrantholder, then by an appraiser chosen by the Company and reasonably satisfactory to the Warrantholder. Any determination of the Market Price by an appraiser shall be based on a valuation of the Company as an entirety without regard to any discount for minority interests or disparate voting rights among classes of Capital Stock.

“Person” means any individual, firm, corporation, partnership, limited liability company, trust, incorporated or unincorporated association, joint venture, joint stock company, governmental authority or other entity of any kind, and shall include any successor (by merger or otherwise) of such entity.

“QPO” means an underwritten public offering (underwritten by a reputable underwriter of national reputation) of shares of Common Stock registered pursuant to the Securities Act.

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“Securities Act” means the Securities Act of 1933, as amended, and the rules and regulations of the United States Securities and Exchange Commission thereunder.

“Stockholders’ Agreement” means the Third Amended and Restated Stockholders’ Agreement, dated as of June 10, 2008, by and among the Company and each other stockholder of the Company party thereto, as amended from time to time.

12. Miscellaneous Provisions.

12.1 Entire Agreement. This Warrant constitutes the entire agreement between the Company and the Warrantholder with respect to this Warrant.

12.2 Binding Effect; Benefits. This Warrant shall inure to the benefit of and shall be binding upon the Company and the Warrantholder and their respective permitted successors and assigns. Nothing in this Warrant, expressed or implied, is intended to or shall confer on any person other than the Company and the Warrantholder, or their respective permitted successors or assigns, any rights, remedies, obligations or liabilities under or by reason of this Warrant.

12.3 Section and Other Headings. The section and other headings contained in this Warrant are for reference purposes only and shall not be deemed to be a part of this Warrant or to affect the meaning or interpretation of this Warrant.

12.4 Notices. All notices, demands and other communications provided for or permitted hereunder shall be made in writing and shall be by registered or certified first-class mail, return receipt requested, telecopier, courier service, overnight mail or personal delivery:

If to the Company:

Aspen Aerogels, Inc.

30 Forbes Road, Building B

Northborough, MA 01532

Telephone: (508)  ###-###-####

Facsimile: (508)  ###-###-####

Attention: Chief Executive Officer

with a copy (which shall not constitute notice) to:

Edwards Angell Palmer & Dodge LLP

111 Huntington Avenue

Boston, MA 02199

Telephone: (617)  ###-###-####

Facsimile: (888)  ###-###-####

Attention: Christopher W. Nelson, Esq.

If to the Warrantholder:

[IMPORT WARRANTHOLDER ADDRESS INFORMATION]

All such notices and communications shall be deemed to have been duly given when delivered by hand, if personally delivered; when delivered by courier or overnight mail, if delivered by commercial courier service or overnight mail; five (5) Business Days after being deposited in the mail, postage prepaid, if mailed; and when receipt is mechanically acknowledged, if telecopied. Any party may, by notice given in accordance with this Section 12.4, designate another address or Person for receipt of notices hereunder.

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12.5 Issuance Tax, Attorneys’ Fees, Notices, Successors

(a) Issuance Tax. The issuance of certificates for shares of Common Stock upon exercise of this Warrant shall be made without charge to the holder hereof for any issuance tax in respect hereof, provided that the Company shall not be required to pay any tax which may be payable in respect of any transfer involved in the issuance and delivery of any certificate in a name other than that of the holder of this Warrant.

(b) Attorneys’ Fees. In the event of an action, suit or proceeding brought under or in connection herewith, the prevailing party therein shall be entitled to recover from, and the other party hereto agrees to pay, the prevailing party’s costs and expenses in connection therewith, including reasonably attorneys’ fees.

(c) Registration Agreement. The Warrantholder shall be entitled to all of the rights (excluding demand registration rights) set forth in that certain Third Amended and Restated Registration Rights Agreement (as the same may be amended from time to time) dated as of June 10, 2008 (the “Registration Rights Agreement”) among the Company and the parties thereto on the terms and conditions set forth therein, as if such terms and conditions were set forth in this Warrant. A copy of said Registration Rights Agreement has been provided to the Warrantholder. Simultaneously with the execution of this Warrant, the Warrantholder shall execute, at the option of the Company, either a counterpart signature page to such Registration Rights Agreement, or an amendment to the Registration Rights Agreement, either of which document shall add the Warrantholder as a party thereto and give the Warrantholder all registration and other rights (excluding demand registration rights) as and to the extent provided therein to “Investors” thereunder. Company and the Purchaser hereby further agree that for the purposes of the Registration Rights Agreement, the Shares issuable upon exercise of this Warrant are “Registrable Securities,” as that term is defined in the Registration Rights Agreement.

(d) Stockholders’ Agreement. The Warrantholder shall be entitled to all of the rights (excluding rights of first refusal) set forth in the Stockholders’ Agreement, as if such terms and conditions were set forth in this Warrant. A copy of said Stockholders’ Agreement has been provided to the Warrantholder. Simultaneously with the execution of this Warrant, the Warrantholder shall execute, at the option of the Company, either a counterpart signature page to such Stockholders’ Agreement, or an amendment to the Stockholders’ Agreement, either of which document shall add the Warrantholder as a party thereto and give the Warrantholder all rights and be subject to the obligations (excluding rights of first refusal) as and to the extent provided therein to “Investors” thereunder. Company and the Purchaser hereby further agree that for the purposes of the Stockholders’ Agreement, the Shares issuable upon exercise of this Warrant will be deemed to be Stock as that term is defined in the Stockholders’ Agreement.

12.6 Severability. Any term or provision of this Warrant which is invalid or unenforceable in any jurisdiction shall, as to such jurisdiction, be ineffective to the extent of such invalidity or unenforceability without rendering invalid or unenforceable the terms and provisions of this Warrant or affecting the validity or enforceability of any of the terms or provisions of this Warrant in any other jurisdiction.

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12.7 GOVERNING LAW. ALL ISSUES CONCERNING THIS WARRANT SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAW OF THE STATE OF DELAWARE, WITHOUT REGARD TO THE CONFLICTS OF LAW PRINCIPLES THEREOF.

12.8 Rights as Shareholders. No holder of this Warrant, as such, shall be entitled to vote or receive dividends or be deemed the holder of Common Stock or otherwise be entitled to any voting or other rights as a shareholder of the Company, until this Warrant shall have been exercised and the Shares purchasable upon the exercise shall have become deliverable, as provided herein.

13. Disposition of Warrant or Shares of Common Stock

With respect to any offer, sale or other transfer or disposition of this Warrant or any shares of Common Stock acquired pursuant to the exercise of this Warrant prior to registration of such shares, the holder hereof and each subsequent holder of this Warrant agrees to give written notice to the Company prior thereto, describing briefly the manner thereof, together with a written opinion of such holder’s counsel (if reasonably requested by the Company and reasonably satisfactory to the Company) to the effect that (i) such offer, sale or other transfer or disposition may be effected without registration or qualification of this Warrant or such shares of Common Stock under the Act as then in effect, and (ii) indicating whether or not under the Act this Warrant or the certificates representing such shares of Common Stock to be sold or otherwise transferred or disposed of require any restrictive legend thereon in order to ensure compliance with the Act; provided, however, that a written opinion of holder’s counsel shall not be required in connection with any sale pursuant to Rule 144. This Warrant or the certificates representing the shares of Common Stock thus transferred (except a transfer pursuant to Rule 144) shall bear a legend as to the applicable restrictions on transferability in order to insure compliance with the Act, unless in the aforesaid opinion of counsel for the holder, such legend is not required in order to insure compliance with the Act. Upon any valid transfer of this Warrant or portion thereof, Company agrees to reissue the Warrant (or Warrants in the case of a partial transfer) and/or the Shares receivable upon the exercise hereof, and if the legend is not required, such re-issuance shall be without said legend. Nothing herein shall restrict the transfer of this Warrant (or any portion hereof) or the certificates representing the shares of Common Stock acquired pursuant to the exercise of this Warrant by the initial holder hereof or any successor holder to (i) any affiliate of such holder, including without limitation any partnership affiliated with such holder, any partner of any such partnership or any successor corporation to the holder hereof as a result of a merger or consolidation with or a sale of all or substantially all of the stock or assets of the holder, (ii) any Person in a public offering pursuant to an effective registration statement under the Act, (iii) to any other Person to the extent that the transfer to such Person is exempt from the registration requirements of the Act and such Person agrees in writing to be bound by all of the restrictions on transfer contained herein, or (iv) any Person or Persons if the holder hereof shall also transfer or assign all or part of its interest in the Financing Arrangement, and such Person agrees in writing to be bound by all of the restrictions on transfer contained herein provided, however, that no such transfer may be made to any direct competitor of the Company, which shall mean a Person engaged in the research, manufacture or sale of aerogels, aerogel based products or insulation products. Any transfer described above must be made in compliance with all applicable federal and state securities laws. The Company may issue stop transfer instructions to its transfer agent in connection with the foregoing restrictions.

14. Warrantholder’s Representations

The Warrantholder acknowledges that it has had access to all material information concerning the Company which it has requested. The Warrantholder also acknowledges that it has had the opportunity to, and has to its satisfaction, questioned the officers of the Company with respect to its

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investment hereunder. The Warrantholder represents that it understands that the Warrant and the Common Stock are speculative investments, that it is aware of the Company’s business affairs and financial condition and that it has acquired sufficient information about the Company to reach an informed and knowledgeable decision to acquire the Warrant. The Warrantholder is purchasing the Warrant and any Common Stock issued upon exercise thereof for investment for its own account only and not with a view to, or for resale in connection with, any “distribution” thereof in violation of the Act or applicable state securities laws. The Warrantholder further represents that it understands that the Warrant and Common Stock have not been registered under the Act or applicable state securities laws by reason of specific exemptions therefrom, which exemptions depend upon, among other things, the bona fide nature of the Warrantholder’s investment intent as expressed herein. The Warrantholder is an “accredited investor” as defined in Regulation D promulgated under the Act.

15. Company’s Representations.

As a material inducement to the Warrantholder to purchase this Warrant, the Company hereby represents and warrants that:

(a) The Company shall have made all filings under applicable federal and state securities laws necessary to consummate the issuance of this Warrant pursuant to this Agreement in compliance with such laws, except for such filings as may be made properly after the Grant Date.

(b) The copies of any existing stock purchase agreements and investor’s rights agreements and the Company’s charter documents and bylaws which have been furnished to Warrantholder or the Warrantholder’s counsel reflect all amendments made thereto at any time prior to the date hereof and are correct and complete.

(c) With respect to the issuance of this Warrant or the issuance of the Common Stock upon exercise of the Warrant, there are no statutory or contractual stockholders preemptive rights or rights of refusal, except for any such rights contained in any stock purchase agreement and/or investor’s rights agreements which have been waived. The Company has not violated any applicable federal or state securities laws in connection with the offer, sale or issuance of any of its capital stock, and the offer, sale and issuance of this Warrant does not require registration under the Act or any applicable state securities laws. To the best of the Company’s knowledge, there are no agreements between the Company’s stockholders with respect to the voting or transfer of the Company’s capital stock or with respect to any other aspect of the Company’s affairs.

(d) The execution, delivery and performance of this Warrant have been duly authorized by the Company. This Warrant constitutes a valid and binding obligation of the Company, enforceable in accordance with its terms. The execution and delivery by the Company of this Warrant, the issuance of the Common Stock upon exercise of the Warrant, and the fulfillment of and compliance with the respective terms hereof and thereof by the Company, do not and shall not (i) conflict with or result in a breach of the terms, conditions or provisions of, (ii) constitute a default under, (iii) result in the creation of any lien, security interest, charge or encumbrance upon the Company’s capital stock or assets pursuant to, (iv) give any third party the right to modify, terminate or accelerate any obligation under, (v) result in a violation of, or (vi) require any authorization, consent, approval, exemption or other action by or notice or declaration to, or filing with, any court or administrative or governmental body or agency pursuant to, the charter or bylaws of the Company or any subsidiary, or any law, statute, rule or regulation to which the Company or any subsidiary is subject, or any agreement, instrument, order, judgment or decree to which the Company or any subsidiary is subject, except for any such filings required under applicable “blue sky” or state securities laws or required under Regulation D promulgated under the Act.

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16. Company Financial Information.

Until such time as the Company shall have satisfied all of its obligations under the Financing Arrangement, Company shall deliver to Warrantholder such financial information as is required under the terms of the Financing Arrangement. From and after the date that the Company shall have satisfied all of its obligations under the Financing Arrangement, and notwithstanding any other agreement to the contrary between the parties hereto, the Company shall deliver to the Warrantholder (so long as the Warrantholder holds all or any portion of the Warrant or any Preferred Stock or any shares of Common Stock issuable upon conversion of the Preferred Stock) all of the financial and other information delivered or required to be delivered by the Company to any of its stockholders, in their capacities as stockholders. All such financial and other information shall be delivered pursuant to this Section on a timely basis, but no later than 30 days after each fiscal quarter end for quarterly statements and no later than 120 days after each fiscal year end for annual statements.

*         *         *         *         *

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IN WITNESS WHEREOF, the Company has caused this Warrant to be signed by its duly authorized officer.

Dated: [IMPORT ISSUE DATE]

Exhibit A: Exercise Form

(To be executed upon exercise of this Warrant)

[1. The undersigned hereby elects to purchase                     shares of Common Stock of Company pursuant to the terms of the attached Warrants, and tenders herewith payment of the purchase price of such shares in full.]

[1. The undersigned hereby elects to purchase                     shares of Common Stock of Company pursuant to a non-cash exercise of the Warrant as provided in Section 2 of the Warrant.]

2. Check here if applicable:                     The undersigned confirms that this exercise is made in connection with the occurrence of a public offering, sale or merger of the Company, and the undersigned further elects to condition this exercise of the Warrant upon the consummation of said public offering, sale or merger of the Company. This exercise shall not be deemed to be effective until the consummation of such transaction. In the event that transaction is not consummated within 45 days of the targeted date of the transaction, the undersigned will advise Company whether or not this exercise should be deemed rescinded.

2. Please issue a certificate or certificates representing said shares in the name of the undersigned or in such other name or names as are specified below:

[IMPORT WARRANTHOLDER ADDRESS INFORMATION]

3. The undersigned represents that the aforesaid shares are being acquired for the account of the undersigned for investment and not with a view to, or for resale in connection with, the distribution thereof and that the undersigned has no present intention of distributing such shares.

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