ASPEN AEROGELS,INC. CAPITAL STOCK PURCHASE WARRANT

Exhibit 4.5

THIS WARRANT AND ANY SECURITIES ACQUIRED UPON THE EXERCISE OF THIS WARRANT HAVE BEEN ACQUIRED FOR INVESTMENT AND HAVE NOT BEEN REGISTERED UNDER APPLICABLE U.S. OR NON-U.S. SECURITIES LAWS. NEITHER THIS WARRANT, SUCH SECURITIES NOR ANY INTEREST THEREIN MAY BE SOLD, TRANSFERRED, PLEDGED OR HYPOTHECATED EXCEPT IN ACCORDANCE WITH THE PROVISIONS OF REGULATION S OF THE SECURITIES ACT, UNDER THE REGISTRATION PROVISIONS OF THE SECURITIES ACT OR PURSUANT TO AN EXEMPTION FROM REGISTRATION UNDER THE ACT. HEDGING TRANSACTIONS INVOLVING THIS WARRANT, SUCH SECURITIES OR ANY INTEREST THEREIN MAY NOT BE CONDUCTED UNLESS IN COMPLIANCE WITH THE SECURITIES ACT.

THE SALE, ASSIGNMENT, HYPOTHECATION, PLEDGE, ENCUMBRANCE OR OTHER DISPOSITION AND VOTING OF ANY OF THE SHARES OF CAPITAL 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, AS AMENDED OR AMENDED AND RESTATED FROM TIME TO TIME, AMONG THE COMPANY AND CERTAIN OF ITS STOCKHOLDERS. THE COMPANY WILL NOT REGISTER THE TRANSFER OF SUCH SHARES OF CAPITAL 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.

CAPITAL STOCK PURCHASE WARRANT

This document (this “Warrant”) dated as of June 10, 2008 certifies that, for good and valuable consideration, Aspen Aerogels, Inc., a Delaware corporation (the “Company”), grants to [                    ] or any successor or permitted assign of such Person (the “Warrantholder”), the right to subscribe for and purchase from the Company, on or before the Expiration Time (as defined below), up to [                    ] validly issued, fully paid and nonassessable shares of Common Stock of the Company (as may be adjusted, the “Warrant Shares”) at the exercise price per share of $0.001 (the “Exercise Price”). Capitalized terms used herein which are not specifically defined in other sections of this Warrant, shall have the meanings set forth in Section 10.

1. Warrant Term. Subject to the provisions of Section 2.4, 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 and on or prior to June 10, 2016 (the “Expiration Time”).

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 Warrant Shares then being purchased. The Warrantholder shall be deemed to have become the holder of record of, and shall be treated for all purposes as the record holder of, the Warrant Shares represented thereby (and such Warrant 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 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, along with a check from the Company in lieu of any fractional shares that the Warrantholder would be entitled to purchase under this Warrant. If this Warrant is 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 to this Warrant.

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

2.4 Exercise or Termination upon Corporate Event. If the aggregate Exercise Price, as of the consummation date of any Corporate Event, is equal to or greater than the aggregate value of the securities, cash and other property that would have been received in connection with a 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 automatically 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, and this Warrant shall automatically terminate in connection therewith.

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. As a condition to the exercise of this Warrant and the purchase of the Warrant Shares, the Warrantholder will become a party to the Stockholders’ Agreement pursuant to the form Joinder attached thereto.

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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 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.

3.3 Lock-Up. The Warrantholder agrees not to effect any sale or distribution of Warrant Shares during the seven (7) days prior to and the one hundred eighty (180) days after any Public Offering or such longer period as may be prescribed at such time. For purposes of this Warrant, “Public Offering” shall mean an underwritten public offering pursuant to an effective registration statement under the Securities Act of 1933, as amended, covering the offering and sale by the Company of Common Stock.

4. Reservation and Registration of Warrant Shares. The Company covenants and agrees that 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.

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 this Warrant, shall be subject to adjustment as follows:

5.1 Stock Dividends and Combinations.

(a) If, at any time after the date hereof, the number of shares of Common Stock outstanding is increased by a stock dividend payable in shares of Common Stock or by a subdivision or split-up of shares of Common Stock, then, following the record date for the determination of holders of Common Stock entitled to receive such stock dividend, subdivision or split-up, the Exercise Price shall be decreased and the number of shares of Common Stock issuable on exercise of this Warrant shall be increased in proportion to such increase in outstanding shares.

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(b) If, at any time after the date hereof, the number of shares of Common Stock outstanding is decreased by a combination of the outstanding shares of Common Stock, then, following the record date for such combination, the Exercise Price shall be increased and the number of shares of Common Stock issuable on exercise of this Warrant shall be decreased in proportion to such decrease in outstanding shares.

5.2 Recapitalization, Etc. In the event of any capital reorganization of the Company, any reclassification of the stock of the Company (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 stock dividend or subdivision, split-up or combination of shares), or any consolidation or merger of the Company, this Warrant shall after such reorganization, reclassification, consolidation or merger be exercisable for the kind and number of shares of stock or other securities or property of the Company or of the company resulting from such consolidation or surviving such merger to which the holder of the number of shares of Common Stock deliverable (immediately prior to the time of such reorganization, reclassification, consolidation or merger) upon exercise of this Warrant would have been entitled upon such reorganization, reclassification, consolidation or merger. The provisions of this clause shall similarly apply to successive reorganizations, reclassifications, consolidations and mergers.

5.3 Computations. The computations of all amounts under this Section 5 shall be made assuming all other antidilution or similar adjustments to be made to the terms of all other securities resulting from the transaction causing an adjustment pursuant to this Section 5 have previously been made so as to maintain the relative economic interest of the Warrants vis à vis all other securities issued by the Company.

5.4 Par Value. The Company shall take or cause to be taken such steps as shall be necessary to ensure that the par value per share of Common Stock is at all times less than or equal to the Exercise Price.

6. Transfer and Exchange. If this Warrant is presented to the Company with a request to register a transfer or to exchange it for an equal number of Warrants of other denominations the Company will do so.

7. 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.

8. Ownership of Warrant. The Company may deem and treat the Person in whose name this Warrant is registered as the Warrantholder 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.

9. 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.

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10. 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.

“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.

“Charter” means the Amended and Restated Certificate of Incorporation of the Company, as amended from time to time.

“Common Stock” means the Company’s presently authorized Common Stock, par value $.001 per share, and any stock into or for which such Common Stock may hereafter be converted or exchanged pursuant to the Charter of the Company as amended from time to time as provided by law and in such Charter.

“Corporate Event” means: (i) the sale, transfer, lease, license or other conveyance or disposition of all or substantially all of the Company’s assets; (ii) the Liquidation of the Company; or (iii) the sale, transfer or other disposition of all or substantially all of the Company’s capital stock to a Person or group of Persons that is not an Affiliate of the Company, 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).

“Liquidation” has the meaning set forth in the Charter.

“Person” shall be construed broadly and shall include an individual, a partnership, a corporation, a limited liability company, an association, a joint stock company, a trust, a joint venture, an unincorporated organization, or a governmental entity (or any department, agency, or political subdivision thereof).

“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 the date hereof, as amended, among the Company and certain stockholders of the Company, as the same may be amended, modified or restated from time to time.

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11. Miscellaneous Provisions.

11.1 Entire Agreement. This Warrant and the Stockholders’ Agreement constitute the entire agreement between the Company and the Warrantholder with respect to this Warrant.

11.2 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.

11.3 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.

11.4 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:

to the addressees reflected on the Warrant

register maintained by the Company

All such notices and other communications shall be deemed to have been given and received (i) in the case of personal delivery, on the date of such delivery, (ii) in the case of delivery by telecopy, on the date of such delivery, (iii) in the case of delivery by nationally recognized overnight courier, on the next business day following dispatch and (iv) in the case of mailing, on the third business day following such mailing.

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11.5 Issuance Tax. The issuance of certificates for shares of Common Stock upon exercise of this Warrant shall be made without charge to the Warrantholder 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 Warrantholder.

11.6 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.

11.7 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.

11.8 Rights as Shareholders. The Warrantholder shall not 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 Warrant Shares purchasable upon the exercise shall have become deliverable, as provided herein.

12. Disposition of Warrant or Shares of Common Stock. With respect to any offer, sale or other transfer or disposition of this Warrant or any Warrant Shares acquired pursuant to the exercise of this Warrant prior to registration of such shares, the Warrantholder 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 Securities Act as then in effect, and (ii) indicating whether or not under the Securities 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 Securities 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 Securities Act, unless in the aforesaid opinion of counsel for the holder, such legend is not required in order to insure compliance with the Securities 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 Warrant 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 Warrant Shares acquired pursuant to the exercise of this Warrant by the initial Warrantholder 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

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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 Securities Act, (iii) to any other Person to the extent that the transfer to such Person is exempt from the registration requirements of the Securities Act 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.

13. 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 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 Securities 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 Securities 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 Securities Act.

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

SIGNATURE PAGE TO ASPEN AEROGELS, INC.

COMMON STOCK PURCHASE WARRANT

Exhibit A: Exercise Form

(To be executed upon exercise of this Warrant)

Attention: Chief Financial Officer

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.

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:

[name]

[address]

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.

[name]